In a small skillet heat the remaining ½ teaspoon olive oil on medium low. Whisk the egg whites and eggs together with a tablespoon of water until light and airy and add to the small skillet. Let cook slowly undisturbed until ½ of the eggs have set. Use a spatula to gently lift one side of the omelet so that the runny eggs can pool below, then lay back down the cooked eggs and top the entire top of the omelet with cheese.